An hybrid Imaging-Inversion method applied to potential fields data

The aim of this thesis is to implement an integrated approach of potential fields data analysis, which combines the most employed inversion techniques (Li & Oldenburg, 1996; Pilkington, 1997; Zhdanov, 2002; Fedi et al., 2005) with multi-scale imaging methodologies (i.e. DEXP from Fedi (2007), or others (Fedi and Pilkington, 2012)). Such a complementary approach brings two focal benefits: on the one hand, a multi-scale analysis will provide us with valuable information, e.g. excess mass (magnetization intensity), source shape parameters and source depth, which we will use in the inversion algorithms. On the other hand, the imaging methods could be extended by defining a density/magnetization model based on various type of constraints (density/magnetization contrast, source compactness), as usual for inversion algorithms. Within the scope of this research work, the first above-mentioned aspect has been further investigated, in particular for data coming from “non-simple” sources; their multi-scale behaviour and characteristics have been first analysed and then transferred into the inversion domain. In order to estimate source properties in the multi-scale domain, we referred to the DEXP method (Fedi, 2007) among the imaging approaches, while to perform 2D constrained inversion, we pertained to Li & Oldenburg algorithm (1996), taking into account also the suggestions by Cella et al. (2012). We had to adjust both the reference inversion and the imaging methods we chose for this research work to make them suitable for the integration: first, constraints on source shape, depth and density/magnetization range had to be set in the inversion domain. More specifically, we used one of the outputs of the DEXP transform, called scaling exponent, as an inversion constrain. After defining a preliminary workflow, simple source magnetic anomalies have been synthetically generated to test the proposed approach; then, data caused by more complex sources have been analysed. Finally, some real data from the Bouguer gravity anomaly in the Campanian Plain (Italy) have been examined to have a further confirmation of the effectiveness of the method. Both tests on synthetic and real data showed that adding, as inversion constraints, source information retrieved by a multiscale analysis of the data has a great potential to lead to well-constrained solutions with respect to the source depth and to the horizontal variations of the source-density/magnetization intensity distribution. Throughout the development of the main topic of this thesis, we have also expanded our research field inpecting the upward continuation transform of potential field data. We got involved in this issue because multi-scale imaging methods such as the continuous wavelet transform (Sailhac et al., 2003; Fedi et al., 2010; Fedi and Cascone, 2011), the DEXP transformation (Fedi, 2007) and the multiridge analysis (Cella et al., 2009) involve potential fields data available on a 3D volume, which in turn is generated by upward continuation of data measured at a single - flat or draped - surface. Fedi and Pilkington (2012) show that multiscale imaging techniques are highly influenced by the way the field is upward continued, apart from the depth-weighting factor. Therefore, we defined an alternative approach to upward continue potential field data: the VOCO (Volume Continuation), which has important advantages above existing techniques and is suitable for all types of data continuation between surfaces in the space. VOCO has also been coupled with second order horizontal derivatives of gravimetric data to investigate on the estimate of the sources horizontal limits changing the field continuation height value. Papers regarding the VOCO approach will be introduced in the last chapter and attached at the bottom of this text